Your father may find the idea of wearing diapers to be demeaning, which isn't surprising. However, there's such a great variety of products out there that you should be able
to find one that doesn't look like a diaper.
Look for men's briefs with built-in protection, for example. Essentially, these protective underpants look like men's briefs, but with an insertable pad that will absorb urine. This style may be more acceptable to your father.
If you go this route, you'll want to make sure the briefs fit well. Depending on how advanced your father's dementia is, you might want to ask him to try on some new clothes to see if they fit correctly, and include the briefs in the outfit.
If you're having a hard time convincing your father to wear any form of absorbent protection, you may have to hand over the job to another caregiver, perhaps a temporary one. With someone new, there's no personal history, which may be playing into your father's rejection of your requests.
That said, sometimes parents are just resistant. If this is the case, you may not be able to convince your father, and you'll have to look into other options, such as protecting the furniture where he sits and deodorizing the house.